Signal processing apparatus and method for decision directed symbol synchronisation

ABSTRACT

A signal processing apparatus ( 400;800 ) comprising: a demodulator (e.g. a PSK demodulator) ( 407;900 ) arranged to demodulate a received signal, which carries consecutive symbols (a 1 , . . . , a 4 ) at a symbol rate, wherein the demodulator ( 407;900 ) is arranged, based on sample values of the received signal, to calculate an error value (φ m ) of a given symbol relative to a decision-directed determination of an expected symbol value (I); and a phase-shifter ( 406,409;801;1002,1013 ) arranged to shift the phase of sampling points in time at which points in time, sample values of the received signal is provided to the demodulator ( 407;1000 ). The invention is characterized in that the apparatus ( 400;900 ) comprises a processor ( 408;601;1000 ) arranged to evaluate an error metric (τ), at the symbol rate, for a given symbol as a function of the error value (φ) and symbol values (II), and to determine whether to shift the phase of the sampling points in time based on further evaluation of the error metric (τ). Thereby an optimal sampling instant can be provided based on estimation of Inter Symbol Interference.

This application claims the benefit of the filing date of U.S.Provisional Patent Application No. 60/441,424 filed on Jan. 21, 2003,and claims priority from European Patent Application No. 03388003.0filed on Jan. 17, 2003. This application is a U.S. national stageapplication of International Application No. PCT/EP2003/014486.

This invention relates to a signal processing apparatus comprising: ademodulator arranged to demodulate a received signal, which carriesconsecutive symbols, wherein the demodulator is arranged, based onsample values of the received signal, to calculate an error value of areceived symbol value relative to a decision-directed determination ofan expected symbol value and a reference value, wherein the referencevalue is calculated, based on a calculated error value of previouslyreceived symbols; and a phase-shifter arranged to shift the phase ofsampling points in time, at which points in time sample values of thereceived signal is provided to the demodulator.

Typically, a demodulator finds its application in communicationsequipment where devices are capable of communicating over acommunications channel by establishing a communications link. When thedevices, all the way through the communications link or at intermediateportions of the communications link, operate on digital data, the termdigital communications is typically used to designate the technicalfield.

In digital communications in general and in wireless communications inparticular, the data to be communicated are typically transmitted inbursts. For instance, in the case a communications channel is shared byseveral devices using time division multiple multiplex (TDMA), each userobtains access to the communications channel during time slots, duringwhich a packet of data is transmitted. This type of multiple access isused for instance in the cellular communications system Global Systemfor Mobile communications, GSM, and in the near range communicationssystem Bluetooth™. Both of these systems are digital communicationssystems.

In all types of systems, the transmitter and the receiver must besynchronized in time. In digital communications, however, thissynchronization can be divided into two categories; i.e. framesynchronization and bit synchronization. On the one hand, framesynchronization essentially refers to knowing where a packet of datastarts, and is achieved by transmitting a known sequence of data alongwith the data that it is intended to transmit, i.e. the so-calledpayload data. The known sequence of data is often referred to as aso-called SYNCWORD, but other terms are used like FRAME DELIMITER, etc.On the other hand, bit synchronization refers to what sampling instantis used to make a decision on the symbols within the packet of data. Itshould be noted that a symbol typically represents one or several bits(typically 1-3 (4) bits). On a so-called physical layer of thecommunications link, the symbols are represented by (analogue) amplitudeand/or phase values of an electromagnetic signal. Hence, in bringingthese values into a digital domain, the signals must be quantified bysampling the signal to provide samples of the signal that can beconverted into digital values. The—substantially periodicallyoccurring—points in time at which the signal is sampled are oftendenoted the sampling instant. Bit synchronisation is an important issuein that synchronisation of this sampling instant is crucial inextracting symbol values and thus data from the electromagnetic signal.Bit synchronisation can essentially be carried out in one of three ways.

Firstly, it can be carried out by the aid of a known sequence. This isreferred to as data aided (DA) estimation. This gives good results, butcomes at the cost of the need to transmit more bits.

Secondly, it can be carried out in a decision directed (DD) fashion.This means that a decision on the received data is to be made, and thenestimation as if such decisions were correct shall be carried out. Incase the decisions are in fact correct, the performance would be thesame as for the data aided estimator, but without the need fortransmitting the extra bits. A problem with decision directed estimationarises when the decisions are erroneous, since then the performance of adecision directed estimator is degraded considerably.

Thirdly, one can use non-data aided (NDA) estimation. In this type ofestimators, the effect of the actual data is typically removed by sometype of (non-linear) function. One example of this is tat, in case themodulation is M-ary phase shift keying (M-PSK), then the actual data canbe removed by taking the received signal to the Mth power. The drawbackof non-data aided estimation is that the operation required removing theactual data results in noise enhancement, thus yielding a worseperformance than data aided estimation.

In the following, the estimation is decision directed. The reason simplybeing that in many systems no known data are available, that there is ahigh probability that the decisions are correct, and even if somedecisions would be erroneous, this is believed to only cause a gracefuldegradation of the performance rather than causing the algorithms tocompletely fail to function.

To further describe the background of the invention, consider thesituation that both frame synchronisation and bit synchronisation havebeen achieved, but where it is desirable to improve the bitsynchronisation. There are two different reasons why this may be thecase. Firstly, the original bit synchronisation may not have been goodenough. Secondly, throughout the reception of the packet, time-drift mayhave caused the originally chosen sampling instant to no longer beoptimal. In either of these cases, it is desirable to update the usedsampling phase in order to improve the performance of the overallcommunications system and in particular a receiver.

Since the performance of a system can be severely degraded in case anon-optimal sampling instant is used, the problem of adjusting the usedsampling instant is not new, but has been worked on by others.

WO 97/03507 discloses a method and an apparatus for recovering a timingphase and frequency of a sampling clock signal in a receiver. This isbased on minimizing a mean squared error due to un-cancelled precursorinter symbol interference; a precursor is a sample that is located onesample (corresponding to one symbol) ahead of an optimum samplinginstant of a given symbol and which value, ideally, is not affected bythe impulse representing the given symbol. A detected symbol error iscorrelated with a signal obtained from the received signal. Thiscorrelation function provides an approximate of the time instant wherethe mean squared error approaches its minimum at which point anunambiguous zero crossing of the correlation function is obtained. Fromthis zero crossing a desired sampling instant is determined. A decisionfeedback equalizer (DFE) implements this recovery of the samplingphase/frequency.

However, this involves a high computational effort in that embodimentsof this timing recovery principle requires calculation of thecorrelation function, AG, for each received symbol pulse to provide aphase adjustment signal.

Hence, the prior art involves the problem that an excessivecomputational effort is required for the prior art principle to work.Additionally, delay elements and filter coefficients of the equalizeroccupy critical circuit space. Moreover, precise identification of thezero crossing can be critical when realistic noise levels are present inthe received signal.

It is therefore an object of the present invention to provide a methodand an apparatus of low complexity that accomplish the above-mentionedadjustment of the sampling phase.

The above and other problems are solved when the signal processingapparatus mentioned in the opening paragraph is characterized incomprising a processor arranged to evaluate an error metric, at thesymbol rate, for a given symbol as a function of the error value andsymbol values, and to determine whether to shift the phase of thesampling points in time based on further evaluation of the error metric.

Consequently, a metric that is simple to calculate and is indicative ofwhether the sampling phase is advanced or retarded relative to anoptimal sampling phase in provided. Since the metric is calculated basedon signals typically available in a demodulator the invention isimplemented in a very cost-efficient way. Additionally, since the metricneeds only be calculated at symbol rate the computational effortinvolved is very limited.

Since the error metric is a function of the error value and the symbolvalues, the latter corresponding to the data the symbols represent, theerror metric can be configured to take into account an expected effectof Inter Symbol Interference. Hence, the error metric can be updatedaccording to the magnitude of the expected Inter Symbol Interference.

Moreover, the invention relates to a mobile telephone comprising asignal processing apparatus as set forth above; and a method ofprocessing a signal.

The present invention will be described in more detail in the followingdetailed description of the invention and with reference to thedrawings, in which:

FIG. 1 shows a block diagram model of a communications link;

FIG. 2 shows four symbols of a π/2-rotated BPSK signal mapped into arespective IQ-plane;

FIG. 3 shows I- and Q components of a π/2-rotated BPSK signal in thetime-domain;

FIG. 4 shows a block diagram for a digital receiver;

FIG. 5 a shows an eye-pattern for a π/2-rotated Binary Phase ShiftKeying (BPSK) modulated signal;

FIG. 5 b shows a zoom-in of an eye-pattern for a π/2-rotated BPSKmodulated signal;

FIG. 6 a shows processor according to the invention;

FIG. 6 b shows a flowchart for an algorithm according to the invention;

FIG. 7 shows a block diagram model of a semi-coherent demodulator;

FIG. 8 shows a semi-coherent demodulator according to the invention foradjusting the sampling phase according to the invention;

FIG. 9 shows a more detailed block diagram of a semi-coherentdemodulator;

FIG. 10 shows a detailed block diagram of a semi-coherent demodulatoraccording to the invention.

As an introduction to the detailed description, a communications link, areceiver, and some demodulation aspects are explained.

FIG. 1 shows a block diagram model of a communications link. The blockdiagram model illustrates a communications link in a simple way. Thecommunications link comprises an ideal transmitter 108 capable ofmodulating a carrier signal with a sequence of symbols a_(m) to providea communications signal that can be transmitted over a communicationschannel CH 104. A base band circuitry (not shown) provides the sequenceof symbols a_(m) to a transmitter filter TxF 101, which provides afiltered sequence of symbols to a mixer 102. By means of the mixer 102,a carrier signal C1 is modulated with the filtered sequence to providethe communications signal. The communications signal is amplified bymeans of a power amplifier PA 103 prior to being transmitted via thecommunications channel 104.

At the receiver side of the communications channel 104 the communicationlink comprises an ideal receiver 109 which is capable of demodulatingthe communications signal to provide a base band signal Yk to a baseband circuitry (not shown). The communications signal is received andamplified in a low noise amplifier 105 wherefrom it is input to a mixer106. By means of the mixer 106 the communications signal is mixed with asignal C2 to thereby provide a down-converted input signal to a receiverfilter RxF 107, which in turn provides the base band signal y_(k).

Typically, the bandwidth of the communication channel sets the upperlimit for the rate at which symbols can be transmitted. Since, theinformation to be transmitted is in digital form, a digital signal withsquare wave pulses can be used to modulate the carrier signal.Conceptually, supplying a carrier signal and the digital signal to amixer, which thereby provides a modulated signal, carries this out.However, the modulated signal will occupy a relatively large bandwidthas a result of the carrier being mixed with a square wave signal.Therefore, the digital square pulses in the digital signal are shapedbefore they are mixed with the carrier signal. The square wave pulsesare shaped with the transmitter filter TxF 101 that, on the one hand andas desired, limits the bandwidth and consequently, on the other hand,extends the length of the pulse in the time domain. By this technique,also denoted ‘pulse shaping’ or ‘softening’, the transmitted bandwidthis reduced because it produces greatly diminished side-componentsfarther away from the carrier. In order to optimise the achievablesymbol rate on the channel, the receiver filter RxF 107 is matched withthe transmitter filter TxF 101 to have, in combination, an impulseresponse that allows for transmitting symbol pulses with a repetitionperiod that is smaller than the length of the impulse response withoutdestroying the information that a symbol pulse carries.

To characterize the impulse response of the receiver filter RxF and thetransmitter filter TxF in combination (that is, the convolution of theimpulse responses of the receiver filter and the transmitter filter)relative to the symbol repetition period; the impulse response must haveside-lobes in the time-domain and the impulse response must have asufficiently long time duration relative to the repetition period as toallow for a temporal overlap between a pulse and side-lobes of anotherpulse.

Commonly, the rate and the phase of the symbol pulses are configuredsuch that succeeding and preceding symbol pulses occur incidentally withzero-crossings of a present symbol pulse. Preferably, a filter with apulse response corresponding to a so-called raised cosine pulse is usedfor shaping the digital signal.

In the time-domain the raised cosine pulse is defined by the following:

${r(t)} = {\sin\;{{c\left( \frac{t}{T} \right)} \cdot \left\lbrack \frac{\cos\left( \frac{\alpha \cdot \pi \cdot t}{T} \right)}{1 - \left( \frac{2 \cdot \pi \cdot t}{T} \right)^{2}} \right\rbrack}}$wherein r is a function of time t, T is a time period, and α is aso-called roll-off parameter. Applying the principle of configuring therate and the phase of the symbol pulses such that succeeding andpreceding symbol pulses occur incidentally with zero-crossings of apresent symbol pulse implies that the repetition rate for symbols mustbe integer multiples of T.

In case the applied modulation/demodulation scheme is Phase Shift Keying(PSK), a phase rotation can be applied from one symbol to a next symbol.Thereby, 180 degrees phase shifts between two consecutive symbols areavoided. This, in turn, eliminates signal transitions, between twoconsecutive symbols, through the origin when the signal is depicted inan IQ-plane. It should be noted that such transitions through the originare undesired since they reflect that the signal has zero amplitude andconsequently involves that the receiver and the transmitter must be ableto operate at a larger dynamic range, which is undesirable. Avoidingthese transitions through the origin reduces variations of the envelopeof the signal and thereby provides a steadier signal.

FIG. 2 shows four symbols of a π/2-rotated BPSK signal mapped into arespective IQ-plane. The four symbols a₁, a₂, a₃, and a₄ are mapped intothe IQ-planes A, B, C, and D, respectively. Generally, the binary value“0” is mapped into a signal component value of +1, whereas the binaryvalue “1” is mapped into a signal component value of −1. Please notethat generally subscript numbers or letters, typically m, are used as atime-index to designate a symbol or sample value in a sequence ofvalues.

For the first symbol a₁, it is assumed that the applied rotationψ_(rot)=0. The symbol has a binary value of 1 so consequently the symbolwill located at the coordinate (1,0).

The next symbol a₂ is exposed to a rotation of π/2, hence the binaryvalue of a₂ will be located at (0,1) for a binary value of 1 or at (0,−1) for a binary 0. The binary value of a₂ is 0, so a₂ will be locatedat (0, −1).

In line with this, the applied rotation of a₃ is 2π/2=π. Therefore thebinary value of a₃=1 will be located at (−1,0).

Similarly, the applied rotation of a₄ is 37π/2=−π/2. Therefore thebinary value of a₄=1 will be located at (0,−1).

Having explained the rotation in the IQ-plane, the I- and Q-componentsare illustrated in the time-domain.

FIG. 3 shows I- and Q components of π/2-rotated BPSK signal in thetime-domain. The I- and Q components are shown as decomposed by animpulse response corresponding to a raised cosine function. The impulseresponse corresponds to a raised cosine pulse with roll-off α=0,4. Thecomponents are shown for the above four symbols a₁, a₂, a₃, and a₄ withsymbol values 1; 0; 1; and 1.

The components are shown in the time-domain as a function of time t,wherein time axes 301 are divided into units of the symbol repetitionperiod, and wherein the I- and Q-axes 302 represent amplitude.

By means of arrows 303, sample values of the I-component in the receivedsignal are represented. Similarly, by means of arrows 304, sample valuesof the Q-component in the received signal are represented. The samplevalues occur at symbol rate. Examination of the decomposition of the I-and Q components indicates that sampling the I-component pulse of symbola₂=0 either too early or too late in time will result in constructiveinter symbol interference from the preceding and succeeding symbol.However, sampling the Q-component pulse of symbol a₃=0 either too earlyor too late in time will result in less inter symbol interference fromthe preceding and succeeding symbol since the effect of the pulses willalmost cancel out relatively close (i.e. within 1- 3/16 of a symbolperiod) to an optimal sampling time of a₃.

FIG. 4 shows a block diagram for a digital receiver. The digitalreceiver comprises an antenna 401 for receiving a wirelesscommunications signal and converting the wireless signal to anelectrical signal. Typically, the electrical signal is a high frequencysignal with a signal strength that is weak; hence the electrical signalfrom the antenna 401 is input to a low noise amplifier LNA 402 whereinit is amplified to provide an amplified signal. The amplified signal issupplied to a down-converter circuit Dwn. Conv. 403 wherein thecommunications signal located at a carrier frequency is converted tobase band signal components. In the present embodiment the base bandcomponents consist of an in-phase component 1, and a quadrature phasecomponent Q. Up to this stage of signal processing the signals areanalogue signals, however by means of an analogue-to-digital converter405, the base band components are sampled and converted to a sequence ofdigital sample values. The points in time at which the signal componentsare sampled are controlled by a periodic sampling signal provided by anoscillator, SMP OSC 404. Typically, the signal components are oversampled N times (e.g. N=16 times).

In order to reduce the processing effort needed for subsequentprocessing of the base band components, the sequence of digital samplevalues is decimated (typically N times) by means of decimator DEC 406.Hence, the rate of sample values per signal component is reduced to therate of symbols per signal component. The decimator 406 is controlled bya unit DEC PH 409 for selecting a decimation phase by selecting which ofN samples is to be provided as an output from the decimator. Thereby,the phase can be adjusted in 1/N-sized steps.

In order to provide a precise adjustment of the sampling phase it isdesired to make the adjustment in fine steps, however, when the oversampling ratio (N) is relatively low (e.g. N=1,2,4, or 8), it may leadto an insufficiently small step size to simply select one out of Nsamples. In order to solve this problem, an interpolator may be appliedto provide an interpolated value or multiple interpolated valuesintermediate to the sampled values. The interpolated value or valuesallows for adjustment in smaller steps than the 1/N-sized steps that areavailable without interpolation. It is well-known to a person skilled inthe art to apply such an interpolator.

Following the decimation, digital sample values are provided to ademodulator DEMOD 407. The demodulator contains circuitry for convertingthe sequence of sample values to information bits y_(m). Processor PROC108 implements an algorithm, according to the invention, for adjustingthe phase of samples provided to the demodulator. In a preferredembodiment, the demodulator, wherein data for the algorithm aretypically available, provides input to the algorithm. The phase of thesamples is adjusted by controlling the phase of the decimator and/or thephase and/or frequency of sampling oscillator 204.

For the purpose of demonstrating the present invention in the light of asimple linear model, it is assumed that a linear receiver is employedand that the modulation of a received signal is binary pulse-amplitudemodulation, PAM. Additionally, let h(t) denote the overall impulseresponse as a function of time t for a linear transmission link from anideal transmitter via a transmitter filter, a transmission channelfilter, and a receiver filter. Here, the term filter is used todesignate a linear model. Then, the output r(t) of the receiver filtercan be expressed as:

${r(t)} = {{\sum\limits_{m}{a_{k}{h\left( {t - {mT}} \right)}}} + {n(t)}}$where α_(m)ε{−1,1} is the information to be transmitted from the idealtransmitter and n(t) is additive noise. It then follows that if thereceived signal is sampled at instants τ=τ+mT, where τ is the error insampling time, the samples in the received sequence can be expressed as:

${r\left( {\tau + {mT}} \right)} = {{h(\tau)}\left\lbrack {a_{m} + {\frac{1}{h(\tau)}{\sum\limits_{k \neq 0}{a_{m - k}{h\left( {\tau + {kT}} \right)}}}} + \frac{n\left( {\tau + {kT}} \right)}{h(\tau)}} \right\rbrack}$

For simplicity and with arguments, which will be captured later, thenoise term is removed. Additionally, since the present invention isconcerned with time-tracking as opposed to timing recovery, it can beassumed that τ<<1, so that h(τ)≅h(0) for common pulse shapes of h(t).Consequently, assuming h(0) ≈1, the received signal can be expressed as:

${r\left( {\tau + {mT}} \right)} = {a_{m} + {\sum\limits_{k \neq 0}{a_{m - k}{h\left( {\tau + {kT}} \right)}}}}$It is obvious that the first term is the desired one in that it is thetrue information, whereas the terms in the sum over k, for k≠0 mightcause Inter Symbol Interference, ISI.

In interpreting the above simplified expression it is noteworthy topoint out that:

-   -   1. For many reasonably choices of h(t), h(kT)≅0 for k≠0. Hence,        for small values of τ the Inter Symbol Interference will be very        small. In case h(t) is a raised cosine pulse it will be        identical to zero.    -   2. The ISI will depend on the actual data. If the data are        known, the ISI can be counteracted; this is the principle of a        decision directed equalizer,    -   3. τ can be determined if knowledge of r(τ+mT), h(t), and all        a_(m) is available.

Hence, since h(t) basically is a design parameter, and since r(τ+mT) iswhat is observed as the received signal, these are both known. Actually,this is not completely true since h(t) is assumed to also include thechannel, but assuming the delay-spread of the channel is negligible itis true.

Prima facia, the received data a_(m) is not known. However, by means offor instance a decision-directed demodulator it is possible to estimatethe received data— and often this can be carried out under a highprobability of making a correct decision.

FIG. 5 a shows an eye-pattern for a π/2-rotated Binary Phase ShiftKeying (BPSK) modulated signal. The figure shows multiple signal tracesof the I- and Q-component of a π/2-rotated BPSK modulated signalrecorded for multiple different received data sequences a_(m). Theeye-pattern is based on a signal composed of an impulse response h(t)corresponding to a raised cosine pulse with roll-off α=0,4. The signalcomponents are over sampled OSR=16 times and the ideal sampling momentsare at sampling instants 14, 30, 46 and 62. Considering the I-component,a symbol value of zero is transmitted at sampling instant 30, whereas asymbol value of plus or minus one is transmitted at sampling instants 14and 46.

For a given signal trace at one of the sampling instants 14, 30, 46, and62 the impact of ISI can be evaluated. Considering for instance thesampling interval located around sampling instant 30 and assume this issample m, four major traces can be seen (actually, each major trace ismade up of two minor traces). If sample m−1, sampled at sampling instant14, takes the value minus one and if sample m+1, sampled at samplinginstant 46, takes the same value, then the gradient of the traces aroundsampling instant will be relatively small. This also applies if thevalue of sample m−1 and sample m+1 is plus one. On the contrary, ifsample m+1, sampled at sampling instant 46, takes a different value(than m−1), then the gradient of the traces around the sampling instantwill be relatively large. When the gradient is relatively large theimpact of ISI is also relatively large, and vice versa. Similardeductions are made with reference to FIG. 3.

Since h(τ+kT)≈0; k being an integer number different from k=−1 and k=1,this means that two symbols only; the preceding one and the succeedingone essentially causes the ISI. This simply implies that there are onlytwo non-zero terms in the sum in the simplified expression above. It canalso be seen that in case the sampling error is small, say 1/16 of asymbol (corresponding to one sample when OSR=16) three distincttrajectories are found. In this case the ISI will be close to zero basedon the condition that the previous and the succeeding signals are thesame, due to the fact that ISI introduced by these two symbols then willcancel out. Therefore, the experienced ISI will only become a problemwhen the previous and successive signals differ.

In case the timing error is larger, say 2/16 of a symbol, then fourdistinct ISI trajectories are found due to the ISI, caused by theprevious and successive signal, no longer being able to cancel. However,the resulting ISI is still significantly smaller than when the previousand successive symbols were different. Thus, it is verified that ISI isrelated to sampling error.

Due to an introduced π/2-rotation, symbol decisions are alternately madeon the real part and the imaginary part of the signal. Hence, thedecision on the symbol value is based on the Q-component around samplinginstant 30, whereas it is based on the I-component around samplinginstant 14 and 46.

In case phase modulation is employed, the phase rather than the real andimaginary parts of the signal could have been considered.

Alternatively, the above deductions could have been carried out bydirectly considering the shape of the impulse response h(t).

FIG. 5 b shows a zoom-in of an eye-pattern for a π/2-rotated BPSKmodulated signal. Based on this eye-pattern, the below table 1 can befilled-in.

TABLE 1 shows the relation between received symbols (θ) and theresulting ISI (φ) when the sampling is one and two samples (smp.) toolate. θ_(m−1) θ_(m) θ_(m+1) φ_(m) (+1 smp.) φ_(m) (+2 smp.) −π/2 0 −π/2 0 −0.04 −π/2 0 π/2 0.11 0.21  π/2 0 −π/2  −0.11 −0.21  π/2 0 π/2 0 0.04

Note that due to the π/2-rotation, the phase shift between twoconsecutive symbols will have to be ±π/2. Also, note that it is only thephase shift between the consecutive symbols that are of interest.

φ_(m) is the phase error between the phase value of the mth symbol andthe estimated phase value of the mth symbol. The phase value of the mthsymbol is obtained by demodulation and the estimated phase value isobtained in a decision directed way. Hence, φ_(m) can be determined asthe difference φ_(m)=θ_(m)−{circumflex over (θ)}_(m)·φ_(m) can be usedas a simple measure for updating the sampling time.

However study of table 1 reveals that a simple measure based on φ_(m)only will not contain information whether the sampling time is too earlyor too late. This may result in poor performance of the time tracking.

Hence, a more detailed metric is used:φ_(m)(θ_(m+1)−θ_(m−1))

This metric uses the information in {circumflex over (θ)} to establishinformation whether sampling is too early or too late. Thereby, timetracking can be taken in the correct direction towards reducing φ andconsequently the ISI. An algorithm for updating the sampling time orsampling instant according to the above will be described in thefollowing.

FIG. 6 a shows a processor according to the invention. The processorreceives input from e.g. a demodulator. The input is φ_(m) and θ_(m).The output from the processor is SP, which is a control signal foradjusting the sampling phase. Preferably, the signal is a signal thatindicates whether the sampling phase is to be advanced or retarded orremain unchanged corresponding to SP signal values {+1; −1; 0},respectively. Alternatively, the signal indicates which of a number ofsamples is to be selected from e.g. a decimator. With an over-samplingratio OSR of OSR=16, the signal can indicate that sample no. 8 is to beselected. If the phase is to be advanced, the signal can indicate thatsample no. 9 is to be selected instead.

FIG. 6 b shows a flowchart for a method of updating the sampling time orsampling instant. The method is started in step 601, wherefrom themethod enters step 602.

In step 602 the phase error φ_(m) is calculated as the received phaseθ_(m) minus the ideally received phase {circumflex over (θ)}_(m)obtained in a decision directed fashion. Hence, in step 602 thefollowing expression is evaluated: φ_(m)=θ_(m)−{circumflex over(θ)}_(m).

When the phase error is calculated, it is possible to calculate theerror metric (τ) in step 603: τ_(m)=φ_(m)({circumflex over(θ)}_(m+1)+{circumflex over (θ)}_(m−1))

In a succeeding step 604, a variable τ^(tt) for time tracking isupdated, according to τ^(tt)=τ^(tt)+τ_(m). Please note that superscript‘tt’ is used for designating the variable for time tracking. In case thesampling is performed too late, then τ^(tt) will on average increase,whereas in case the sampling is done too early, then τ^(tt) will onaverage decrease.

In step 605 the absolute value abs(τ^(tt)) of τ^(tt) is compared with athreshold value, T_(drift). In case abs(τ^(tt))>T_(drift), then the usedsampling instant is updated according to the sign of τ^(tt) and τ^(tt)is reset i.e. τ^(rr)=0.

The update of the sampling phase is carried out in either step 608 orstep 607 wherein the phase is decreased or increased, respectively. Thisis expressed by the following pseudo code:

if τ^(tt) > T_(drift) , then SP = SP − 1 τ^(tt) = 0 else, if τ^(tt) <−T_(drift), then SP = SP + 1 τ^(tt) = 0 end

Above, the latter two of the three first steps are used to calculate ametric for the m'th symbol. The fourth step is used to sum the metricsfor all the symbols in order to average out fluctuations due to noise.In case the sampling is done too late, τ^(tt) will on average increase,whereas in case the sampling is done too early, then τ^(tt) will onaverage decrease. Thus, it is reasonable to discard the noise termmentioned in the introductory portion of the detailed description withregard to the linear model since this noise term is averaged out.

Finally, in the fifth step, this accumulated metric is compared withthresholds to determine if an update of the sampling phase should beexecuted. In case an update is executed, the variable for theaccumulated metric is reset to zero.

Thus, there are essentially two steps needed to come up with theprincipal behaviour of the algorithm. First, determine the effect asampling time error has on the phase error for different consecutivesymbols, for instance by generating tables like table 1 above. Second,define an algorithm as the one defined in the five points above whichreflects the content in the abovementioned table.

So far, the invention has been explained with reference to the BPSKmodulation, which requires coherent demodulation. In the following, theinvention is to be explained with reference to DPSK modulation, whichallows for using non-coherent, fully coherent or semi-coherentdemodulation. However, it is noted that especially when semi-coherentdemodulation is applied the invention can be embodied with very littleadded complexity since the invention can make use of signals availablein a semi-coherent demodulator.

Before explaining how to implement this sampling time tracking algorithmin connection with a (semi-coherent) demodulator, the working principleof a known semi-coherent demodulator will be explained.

FIG. 7 shows a block diagram model of a semi-coherent demodulator.

The demodulator 700 constitutes a part of the receiver and it mayreceive its input in digital form, from the receiver filter. In case thereceiver provides signal components (e.g. I and Q components)representing a signal in the Cartesian or Euclidian system ofcoordinates, the signal is converted to a phase representation. Henceinput to the demodulator is in the form of phase values. Magnitudeinformation may be provided as a result of the conversion, but thisinformation is typically discarded as regards the demodulator.

In case the demodulator operates in a steady state and no update of thephase is needed, the expected reference phase ψ^(ref) for a symbol θ_(m)is the phase of the previous symbol θ_(m−1) The phase of the previoussymbol is actually not known, but making a tentative decision based onthe realised phase of symbol θ_(m−1) provides an estimate {circumflexover (θ)}_(m−1). This tentative decision to provide the estimate iscarried out in the unit 601. The estimate is feed forward to an adder702, wherein the estimate is subtracted from the realised phase tothereby provide a demodulated signal y_(m). This signal can be decodedby e.g. a look-up table according to the applied modulation/demodulationscheme to retrieve the transmitted information.

In case the demodulator operates in a steady state, but wherein anupdate of the reference phase ψ^(ref) is needed, the expected phase forthe symbol θ_(m) is the phase of the previous symbol θ_(m−1) compensatedfor an update of the phase. Typically, the update is estimated to be thedifference between the decision-directed estimate of the phase and therealised phase of symbol θ_(m).

As the name suggests, this demodulator is neither fully non-coherent norfully coherent. The amount of coherence is determined by a coherenceparameter α. The basic idea with a semi-coherent demodulator is to buildup a phase reference in a decision directed fashion. In a fullynon-coherent case, this phase reference would in fact be the phase ofthe previously received symbol, thus being as noisy as the phase of thereceived signal itself. In case of a fully coherent demodulator, thephase reference would be noiseless. By creating a phase reference byusing several symbols, this reference becomes less noisy. Actually, theidea behind the semi-coherent demodulator is to create a phase referencethat is less noisy than the signal itself, but still does not requireperfect knowledge of the phase, which would be the case if coherentreception was used.

The semi-coherent demodulator is configured to cooperate with simplemeans (e.g. a so-called slicer) for making a tentative decision on whichone out of specified signal points a received signal point tend to be.

If, for instance, DQPSK modulation is used, the specified signal pointsis expected to be 0; π/2; π; and 3π/2, so when making a tentativedecision, boundaries for making a decision are located at π/4; 3 π/4;5π/4; and 7π/4. Since DQPSK involves differential modulation, a phaserotation of the entire signal constellation will cancel out once thedifference between two symbols is taken. However, if the signal isrotated by the channel e.g. π/4, then it is not possible to make areliable tentative decision—a received signal point may in this case belocated at the decision boundary. The phase reference, designated bysymbol ψ^(ref) is an estimate of this rotation. In order to cooperatewith a simple slicer, this rotation is removed before the tentativedecision is taken by the slicer.

In case a frequency offset is present, a (true) phase rotation isinherently present. The phase reference ψ^(ref) shall vary in the sameway as this true rotation in order to be able to remove this truerotation. If the frequency offset is positive, the phase referenceψ^(ref) will increase accordingly. The update of ψ^(ref) is typicallycarried out by some type of low-pass filtering, which can be implementedby a simple IIR filter (or alternatively a FIR filter). An example ofthe update is based on the following:ψ_(m) ^(ref)=α·ψ_(m−1) ^(ref)+(1−α)(ψ_(m) ^(ref)−φ_(m))

Wherein 0<α<1. If α≈1 the reference is heavily filtered, whereas if α=0no filtering at all takes place.

The above expression can also be rewritten:ψ_(mm) ^(ref)=ψ^(ref) _(m−1)+(1−α)(ψ_(m) ^(ref)−{circumflex over(θ)}_(m)−ψ^(ref) _(m−1))ψ^(ref) _(m)=ψ^(ref) _(m−1)+(1−α)(φ_(m))where φ_(k) is the phase error obtained from θ_(m) after the referencephase ψ_(m) ^(ref) has been removed.

In a fully non-coherent demodulator the feed-forward loop would consistof a simple delay element only, so that the reference for θ_(m) would beθ_(m−1). Here, the reference consists of two terms, corresponding to adecision made for the previous symbol, θ_(m−1) and a phase referenceψ_(mm) ^(ref).

Having discussed the coherence principle of the demodulator, thedecoding principle of a (semi-coherent) π/2-rotated DPBSK demodulatorcan be expressed by the below seven (1-7) steps:

Step Expression: 1. ψ_(m)^(rot) = (ψ_(m − 1)^(rot) + π/2)mod  2π 2.θ_(m)^(derot) = θ_(m) − ψ_(m)^(rot) − ψ_(m − 1)^(ref) 3.${\hat{\theta}}_{m}^{derot} = \left\{ \begin{matrix}{{0\text{:}\mspace{14mu}{\theta_{m}^{derot}}} < {\pi/2}} \\{\pi\text{:}\mspace{14mu}{otherwise}}\end{matrix} \right.$ 4. θ̂_(m) = θ̂_(m)^(derot) + ψ_(m)^(rot) 5.ϕ_(m) = θ_(m) − (θ̂_(m) + ψ_(m − 1)^(ref))  (i.e.  a   phase  error  for  present  symbol)6.ψ_(m)^(ref) = ψ_(m − 1)^(ref) + (1 − α)ϕ_(m)  (i.e. a  phase  reference)7. y_(m) = θ_(m) − θ̂_(m − 1) − ψ_(m)^(ref) − π/2

Step 1 above reflects that the received signal is a π/2-rotated BPSKsignal, wherein a succeeding symbol is rotated π/2 relative to apreceding symbol. The absolute phase rotation applied for symbol m isequal to the absolute phase rotation of the previous symbol θ_(m−1) plusthe relative, applied rotation between two consecutive symbols.

Step 2 reflects that the phase of a symbol θ_(m) is rotated back (i.e.de-rotated) to an original phase (i.e. before rotation) and that thereference phase is subtracted, which is required for subsequent step 3.

Step 3 expresses the tentative decision made on the received de-rotatedphase of the mth symbol. The result of this tentative decision is anestimated phase of the mth received symbol. The phase is asserted tohave the value 0 or π, since the modulation in this case is binary.

Step 4 represents an estimate of the phase of the received symbol m,i.e. the estimate of the de-rotated phase plus the applied, relativerotation of π/2.

Step 5 represents a calculation of the phase error for the receivedsymbol θ_(m) In case of perfect coherent reception, ψ^(ref) would bezero so that step 5 would be reduced to φ_(m)=θ_(m)−{circumflex over(θ)}_(m).

Step 6 reflects an update of the accumulated phase error with aweighting factor (1−α) of the phase error for the received symbol θ_(m).

Step 7 shows that the output of the demodulator is generated from thedifference between the phase of the received symbol m and the precedingsymbol θ_(m−). The result is compensated from the applied rotation (π/2)between two consecutive symbols and the phase reference ψ^(ref).

Finally, values of y_(m) can be converted to the binary values one orzero by a binary quantifier e.g. by a so-called slicer.

Having explained the working principle of a semi-coherent demodulator,implementation of the sampling time tracking algorithm in connectionwith a (semi-coherent) demodulator will be described.

FIG. 8 shows a semi-coherent demodulator according to the invention foradjusting the sampling phase according to the invention. The demodulatoris arranged to adjust the sampling phase by controlling decimator 801 tooutput a selected one out of N samples. In case the demodulator operatesin the phase domain, input to the demodulator is in the form of samplesrepresenting phases of symbols. An output signal y_(m) is generated inaccordance with the above-described principle for a semi-coherentdemodulator implemented by unit 803 in combination with adder 802. Notethat the de-rotation is implemented by the unit 803 as opposed to beingimplemented in a separate unit.

Having explained the semi-coherent demodulator according to theinvention the working principle for the time-tracking algorithm will beexplained in more detail below.

Step Expression 8. $\tau_{m - 1}^{e} = \left\{ \begin{matrix}{{- \phi_{m - 1}}\text{:}} & {{{\hat{\theta}}_{m - 2} - {\hat{\theta}}_{m - 1}} = {{- \pi}/2}} \\{\phi_{m - 1}\text{:}} & {{{\hat{\theta}}_{m - 2} - {\hat{\theta}}_{m - 1}} = {\pi/2}}\end{matrix} \right.$ 9. $\tau_{m - 1}^{l} = \left\{ \begin{matrix}{\phi_{m - 1}\text{:}} & {{{\hat{\theta}}_{m} - {\hat{\theta}}_{m - 1}} = {\pi/2}} \\{{- \phi_{m - 1}}\text{:}} & {{{\hat{\theta}}_{m} - {\hat{\theta}}_{m - 1}} = {\pi/2}}\end{matrix} \right.$ 10.τ^(tt) = τ^(tt) > τ_(m − 1)^(l) − τ_(m − 1)^(e) 11. if τ^(tt) >T_(drift), then    SP = SP − 1    τ^(tt) = 0 else, if τ^(tt) <−T_(drift), then    SP = SP + 1    τ^(tt) = 0 end

In step 8 an error metric representing an advanced sampling phase iscalculated. This metric is configured such that the difference betweensample values of two consecutive symbols that precedes a given symboldetermines the value of the metric by determining the sign of thepreceding phase error.

Similarly, in step 9 an error metric representing a retarded samplingphase is calculated. This metric is configured such that the differencebetween sample values of given symbol and a preceding symbol determinesthe value of the metric by determining the sign of the preceding phaseerror.

Step 10 represents an iterative update of a total error metric beingcomposed of the error metric representing a retarded sampling phase andthe error metric representing an advanced sampling phase.

In step 11 a variable, SP, for updating the sampling phase is updated.SP is provided to a decimator for shifting the sampling phase.

FIG. 9 shows a detailed block diagram of a semi-coherent demodulator. Aphase value θ_(m) of a received symbol m is provided by a converter 901that converts an I- and Q-sample value of a symbol to a phase value,which is the phase between the I- and Q-component of the symbol. Thephase value θ_(m) is input, via an adder 903, to a decision unit 904,wherein a decision-directed determination is made to provide anestimated phase value {circumflex over (θ)}_(m). This decision can bemade as a tentative decision based on a threshold value set inphase-domain or IQ-domain. It is assumed that the demodulator operatesin a steady state wherein the decision can be made correctly.

Having provided the estimate, a phase error φ_(m) between the phase ofthe received symbol and the estimated, correct phase {circumflex over(θ)}_(m) can be calculated by means of an adder 907. This phase error isan error for the symbol m, and is consequently as noisy as the phase ofthe symbol. Therefore, this phase error is not suitable for maintaininga phase reference. Thus, a less fluctuating phase reference is createdby means of a low-pass filter 908. Preferably, the low-pass filterimplements the following time-domain transfer function: ψ_(m)^(ref)=ψ_(m−1) ^(ref)+(1−α)φ_(m) wherein the factor (1−α) determines theweight by which the present error influences the reference.

Returning to the input provided to the decision unit 904, via the adder903, the phase value θ_(m) is compensated with the phase referenceψ_(m−1) ^(ref) provided by the low-pass filter 908.

FIG. 10 shows a detailed block diagram of a semi-coherent demodulatoraccording to the invention.

The demodulator comprises a demodulator 1001, e.g. as described above,that receives samples from a controllable decimator 1002. Thedemodulator provides the estimated phase {circumflex over (θ)}_(m) andthe phase error φ_(m).

By means of delay elements 1003 and 1004 {circumflex over (θ)}_(m−1) and{circumflex over (θ)}_(m−2) is provided, respectively. Thereby thedifferences {circumflex over (θ)}_(m−2)−{circumflex over (θ)}_(m−1) and{circumflex over (θ)}_(m)−{circumflex over (θ)}_(m−1) can be provided byadders 1005 and 1006 to units 1007 and 1008, respectively. The units arecalculation units that calculate the error metrics τ_(m−1) ^(e) andτ_(m−1) ^(l) based on which demodulation scheme the demodulator operatesunder and the phase error φ_(m) provided by delay element 1109. Morespecifically, the units implement the steps 8 and 9 of the workingprinciple of the demodulator according to the invention.

The difference between the late and early error metric is provided byadder 1010 and the result thereof is provided to a further adder 1011which together with delay element 1012 iteratively updates the totalerror metric. A decision of whether to update the sampling phase or notis taken by decision unit 1013, which controls decimator 1002.

In case the applied modulation scheme is π/4-rotated DQPSK the abovealgorithms are modified according to the below.

Step Expression 1. ψ_(m)^(rot) = (ψ_(m − 1)^(rot) + π/4)mod  2π 2. seeπ/2 DBPSK 3. ${\hat{\theta}}_{m}^{deret} = \left\{ \begin{matrix}{0:} & {{\theta_{m}^{derot}} < {\pi/4}} \\{{\pi/2}:} & {{\pi/4} \leq \theta_{m}^{derot} < {3{\pi/4}}} \\{\pi:} & {{3{\pi/4}} \leq \theta_{m}^{derot} < {5{\pi/4}}} \\{{{- \pi}/2}:} & {otherwise}\end{matrix} \right.$ 4. see π/2 DBPSK 5. see π/2 DBPSK 6. see π/2 DBPSK7. y_(m) = θ_(m) − θ̂_(m − 1) − ψ_(m − 1)^(ref) − π/4 8.$\tau_{m - 1}^{e} = \left\{ \begin{matrix}{{{- \phi_{m - 1}}\text{:}\mspace{11mu}{sgn}\;\left( {{\hat{\theta}}_{m - 2} - {\hat{\theta}}_{m - 1}} \right)} = {- 1}} \\{{\phi_{m - 1}\text{:}\mspace{11mu}{sgn}\;\left( {{\hat{\theta}}_{m - 2} - {\hat{\theta}}_{m - 1}} \right)} = 1}\end{matrix} \right.$ 9. $\tau_{m - 1}^{l} = \left\{ \begin{matrix}{{{- \phi_{m - 1}}\text{:}\mspace{14mu}{{sgn}\left( {{\hat{\theta}}_{m} - {\hat{\theta}}_{m - 1}} \right)}} = 1} \\{{\phi_{m - 1}\text{:}\mspace{14mu}{{sgn}\left( {{\hat{\theta}}_{m} - {\hat{\theta}}_{m - 1}} \right)}} = {- 1}}\end{matrix} \right.$ 10. see π/2 DBPSK 11. see π/2 DBPSK

In case the applied modulation scheme is non-rotated 8-DPSK the abovealgorithms are modified according to the below.

Non-rotated modulation has the effect on the algorithm for time trackingthat the phases for two consecutive symbols θ_(m−1) and θ_(m), may bethe same or that they might differ by π. Both of these cases cause aproblem the present algorithm for time tracking in that the behaviour ofthe phase does not give much information. For this reason, the metricswill not be updated in case the phase shift between two consecutivesymbols is either 0 or π. For 8-ary modulation, there are eight possiblephase shifts between two symbols, so that on average 75% of the symbolsare still used for time tracking. Below, the algorithm non-rotated8-DPSK is given. Since it is somewhat awkward to let ψ^(rot)=0throughout the algorithm, the notation is adapted accordingly and thesuperscript derot is dropped.

Step Expression 1. — 2. θ_(m) = θ_(m) − ψ_(m − 1)^(ref) 3.${\hat{\theta}}_{m} = \left\{ \begin{matrix}{0:} & {{\theta_{m}} < {\pi/8}} \\{{\pi/4}:} & {{\pi/8} \leq \theta_{m} < {3{\pi/8}}} \\{{\pi/2}:} & {{3{\pi/8}} \leq \theta_{m} < {5{\pi/8}}} \\{{3{\pi/4}}:} & {{5{\pi/8}} \leq \theta_{m} < {7{\pi/8}}} \\{\pi:} & {{7{\pi/8}} \leq \theta_{m} < {9{\pi/8}}} \\{{5{\pi/4}}:} & {{9{\pi/8}} \leq \theta_{m} < {11{\pi/8}}} \\{{3{\pi/2}}:} & {{11{\pi/8}} \leq \theta_{m} < {13{\pi/8}}} \\{{7{\pi/4}}:} & {otherwise}\end{matrix} \right.$ 4. — 5. ϕ_(m) = θ_(m) − θ̂_(m) − ψ_(m − 1)^(ref) 6.ψ_(m)^(ref) = ψ_(m − 1)^(ref) + (1 − α)ϕ_(m) 7.y_(m) = θ_(m) − θ̂_(m − 1) − ψ_(m − 1)^(ref) 8.$\tau_{m - 1}^{e} = \left\{ \begin{matrix}{{{- \phi_{m - 1}}\text{:}\mspace{11mu} 0} > {{\hat{\theta}}_{m - 2} - {\hat{\theta}}_{m - 1}} > {- \pi}} \\{{\phi_{m}\text{:}\mspace{11mu} 0} < {{\hat{\theta}}_{m - 2} - {\hat{\theta}}_{m - 1}} < \pi}\end{matrix} \right.$ 9. $\tau_{m - 1}^{l} = \left\{ \begin{matrix}{{\phi_{m - 1}\text{:}\mspace{11mu} 0} < {{\hat{\theta}}_{m} - {\hat{\theta}}_{m - 1}} < \pi} \\{{\phi_{m}\text{:}\mspace{11mu} 0} > {{\hat{\theta}}_{m} - {\hat{\theta}}_{m - 1}} > {- \pi}}\end{matrix} \right.$ 10. — 11. —

It is noted that the above algorithms for π/4-rotated DQPSK andnon-rotated 8-DPSK can be implemented in connection with the proposedalgorithm for updating the sampling phase.

Generally, it should be emphasized that the invention works on signalsin the IQ-domain as well as on signals in the phase domain.

1. A signal processing apparatus comprising: a demodulator arranged to demodulate a received signal, which carries consecutive symbols at a symbol rate, wherein the demodulator is arranged, based on sample values of the received signal, to calculate an error value of a given symbol relative to a decision-directed determination of an expected symbol value; and a phase-shifter arranged to shift a phase of sampling points in time at which points in time, sample values of the received signal are provided to the demodulator; and a processor arranged to evaluate an error metric, at the symbol rate, for a given symbol as a function of the error value and symbol values, and to determine whether to shift the phase of the sampling points in time based on further evaluation of the error metric; wherein either the error metric is at least one of a function of the phase error value of a given symbol relative to the decision-directed determination of an expected symbol phase value, the phase value of a previous symbol, and the phase of a succeeding symbol; and a function of the phase error of the received symbol multiplied by a difference between the phase of a previous symbol and the phase of a succeeding symbol; or the error metric includes a first term representing that the sampling phase is advanced in time and a second term representing that the sampling phase is delayed in time relative to an optimal sampling phase, wherein the first term is the phase error of the received symbol multiplied by the phase of a succeeding symbol, and the second term is the phase error of the received symbol multiplied by the phase of a preceding symbol; or the error metric expresses Inter Symbol Interference based on an estimate, which is based on an estimated impulse response for a transmission channel over which the symbol is transmitted prior to being input to the signal processing apparatus.
 2. A signal processing apparatus according to claim 1, wherein the error metric is a function of symbol values for symbols preceding and succeeding the given symbol.
 3. A signal processing apparatus according to claim 1, wherein the error metric is a function of expected symbol values.
 4. A signal processing apparatus according to claim 1, wherein the demodulator is configured as a Phase Shift Keying (PSK) demodulator or a Differential Phase Shift Keying (DPSK) demodulator.
 5. A signal processing apparatus according to claim 1, wherein the demodulator is arranged to calculate a variable for time tracking based on an accumulated sum of the error metric.
 6. A signal processing apparatus according to claim 5, wherein the processor is arranged to determine whether to shift the phase, based on the accumulated sum of the error metric.
 7. A signal processing apparatus according to claim 1, wherein the apparatus comprises a sampler arranged to sample the signal at an over sampling ratio OSR, which provides OSR samples per symbol; and the phase-shifter is arranged to control which out of every N samples is to be provided to the demodulator.
 8. A signal processing apparatus according to claim 1, wherein the demodulator is arranged to calculate the error value of a given symbol additionally, relative to a reference value and the reference value is calculated, based on a calculated error value of previously received symbols.
 9. A mobile telephone comprising a signal processing apparatus as set forth in claim
 1. 10. A method of processing a signal, comprising the steps of: demodulating a received signal, which carries consecutive symbols at a symbol rate, and based on sample values of the received signal, calculating an error value of a given symbol relative to a decision-directed determination of an expected symbol value; and shifting the phase of sampling points in time; and evaluating an error metric, at the symbol rate, for a given symbol as a function of the error value and symbol values, and determining whether to shift the phase of the sampling points in time based on further evaluation of the error metric; wherein the error metric is at least one of a function of the phase error value of a given symbol relative to the decision-directed determination of an expected symbol phase value, the phase value of a previous symbol, and the phase of a succeeding symbol; and a function of the phase error of the received symbol multiplied by a difference between the phase of a previous symbol and the phase of a succeeding symbol; or the error metric includes a first term representing that the sampling phase is advanced in time and a second term representing that the sampling phase is delayed in time relative to an optimal sampling phase, wherein the first term is the phase error of the received symbol multiplied by the phase of a succeeding symbol, and the second term is the phase error of the received symbol multiplied by the phase of a preceding symbol; or the error metric expresses Inter Symbol Interference based on an estimate, which is based on an estimated impulse response for a transmission channel over which the symbol is transmitted prior to being input to the signal processing apparatus.
 11. A method of processing a signal according to claim 10, wherein the error metric is a function of symbol values for symbols preceding and succeeding the given symbol.
 12. A method of processing a signal according to claim 10, wherein the error metric is a function of expected symbol values.
 13. A method of processing a signal according to claim 10, wherein the demodulation is Phase Shift Keying (PSK) demodulation or Differential Phase Shift Keying (DPSK) demodulation.
 14. A method of processing a signal according to claim 10, wherein the demodulation comprises calculation of a variable for time tracking based on an accumulated sum of the error metric.
 15. A method of processing a signal according to claim 14, wherein the evaluation comprises determination of whether to shift the phase, based on the variable for time tracking.
 16. A method of processing a signal according to claim 10, further comprising the step of sampling the signal at an over sampling ratio OSR, which provides OSR samples per symbol; and the step of shifting the phase involves controlling which out of every N samples is to be provided for demodulation.
 17. A method of processing a signal according to claim 10, wherein the demodulating includes calculating the error value of a given symbol relative to a reference value, and the reference value is calculated, based on a calculated error value of previously received symbols. 